# Vectors Worksheet

Vector worksheets:

Vectors and scalars are one of the most important chapters or concepts in Mathematics and Physics.

So to sharpen your knowledge here are some Multiple choice questions or objective questions based on vectors and scalars.

The questions here are related to:

Vectors and Scalars

Unit Vector

Components of vectors

Vector product ( Multiplying vectors )

Vector Worksheet:

1> Which of the following is a Vector?

i> Energy

ii> Power

iii> Force

iv> Mass

2> Which of the following is a vector?

i> Time

ii> Work

iii> Heat

iv> Momentum

3>Which of the following is a scalar?

i> Elementary area

ii> Kinetic energy

iii> Weight of a body

iv> Wind velocity

4> Which of the following is a scalar?

i> Electric field

ii> Magnetic Moment

iii> Acceleration

iv> Electrostatic Potential

5> Angular Momentum is:

i> A scalar

ii> A polar vector

iii> An axial vector

iv> Same as torque

6> Moment of inertia is:

i> A scalar

ii> A vector

iii> A tensor

iv> Same as mass

7> $\overrightarrow{F}.\overrightarrow{S}$ is:

i> A scalar

ii> A vector

iii> Neither scalar nor vector

iv> A tensor

8> $\overrightarrow{r} \times \overrightarrow{F}$ is:

i> A scalar

ii> A vector

iii> Neither scalar nor vector

iv> A tensor

9> Which of the following is a scalar?

i> Mass of nucleus

ii> Charge of proton

iii> Wind velocity

iv> Energy of a thermal neutron

10> Pressure is a:

i> A scalar

ii> Axial vector

iii> Polar vector

iv> Neither scalar nor vector

11> Electric Current in a circuit is shown by arrow ; Current is:

i> A scalar

ii> A vector

iii> Sometimes a scalar and sometimes a vector

iv> Neither vector nor a scalar

12> Referring to the following figure, the correct relation is:

Vector MCQ

i> $\overrightarrow{A} + \overrightarrow{B} = \overrightarrow{C}$

ii>$\overrightarrow{B} + \overrightarrow{C} = \overrightarrow{A}$

iii>$\overrightarrow{C} + \overrightarrow{A} = \overrightarrow{B}$

iv>$\overrightarrow{A} + \overrightarrow{B} + \overrightarrow{C} = 0$

13> Referring to the following figure ; the correct relation is:

Vector MCQ

i> $\overrightarrow{A} + \overrightarrow{B} = \overrightarrow{C}$

ii>$\overrightarrow{B} + \overrightarrow{C} = \overrightarrow{A}$

iii>$\overrightarrow{C} + \overrightarrow{A} = \overrightarrow{B}$

iv>$\overrightarrow{A} + \overrightarrow{B} + \overrightarrow{C} = 0$

14>  When two vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ of magnitudes “a” and “b” are added ; the magnitude of resultant vector is:

i> equal to (a+b)

ii> equal to (a-b)

iii> not more than $\sqrt{a^2 + b^2}$

iv> Not greater than (a+b)

15> The minimum numbers of coplanar vectors of unequal magnitudes whose vector sum can be zero is:

1> Two

ii> Three

iii> Four

iv> Any

16> Minimum number of space vectors of unequal magnitudes whose sum is equal to zero is:

i> two

ii> three

iii> four

iv> any

17> Two vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ ie in a plane ; a third vector $\overrightarrow{C}$ lie outside this plane ; then the sum of these three vectors ; $\overrightarrow{A} + \overrightarrow{B} + \overrightarrow{C}$ :

i> Can be zero.

ii> Can never be zero

iii> Lies in the place containing $\overrightarrow{A} + \overrightarrow{B}$

iv> Lies in the plain containing $\overrightarrow{A} - \overrightarrow{B}$

18> Two vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ are such that $| \overrightarrow{A} + \overrightarrow{B} | = | \overrightarrow{A} - \overrightarrow{B} |$ Then the angle between vectors $\overrightarrow{A}$ and $\overrightarrow{B}$  is:

i> zero degree

ii> 60 degrees

iii> 90 degrees

iv> 180 degrees

19> Two vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ are such that $\overrightarrow{A} . \overrightarrow{B} = | \overrightarrow{A} \times \overrightarrow{B} |$ , then the angles between the vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ is:

i> zero degree

ii> 45 degrees

iii> 90 degrees

iv> 180 degrees

20> For the resultant of two vectors to be maximum the angle between them should be:

i> zero degree

ii> 60 degrees

iii> 90 degrees

iv> 180 degrees

21> The magnitudes of sets of three vectors of same type are given below. The resultant of which set can not be zero?

i> 10, 10 , 10

ii> 10, 10 , 20

iii> 10 , 20 , 10

iv> 10 , 20 , 40

22>  Two forces of 6N and 8N can be applied to produce an effect of a single force of:

i> 1 N

ii> 15 N

iii> 11 N

iv> 20 N

23> A car is moving on a road , when rain is falling vertically downward , Rain will strike :

i> Front screen

ii> Wind screen

iii> Both the screens equally

iv> No screen but roof

24> A particle is moving eastward with a velocity of 5m/s . In 10 s the velocity changes to 5 m/s northward. The average acceleration is:

i> Zero

ii> $\dfrac{1}{\sqrt{2}} m/s^2$ toward south-west

iii> $\dfrac{1}{\sqrt{2}} m/s^2$ towards north-west

iv> $1 m/s^2$ towards north

25> Two vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ will be perpendicular if:

i> $\overrightarrow{A} . \overrightarrow{B} = 1$

ii> $\overrightarrow{A} . \overrightarrow{B} =0$

iii> $\overrightarrow{A} \times \overrightarrow{B} = 1$

iv> $\overrightarrow{A} \times \overrightarrow{B} = 0$

26> If $\hat{n}$ is the unit vector along the direction of $\overrightarrow{A}$ then:

i> $\hat{n} = \dfrac{A}{\overrightarrow{A}}$

ii> $\hat{n} = A . \overrightarrow{A}$

iii> $\hat{n} = \dfrac{\overrightarrow{A}}{A}$

iv> $\hat{n} = \overrightarrow{A} . \overrightarrow{A}$

27> A force has magnitude 20N. It’s one rectangular component is 12N , the other rectangular component must be:

i> 8N

ii> 14 N

iii> 16 N

iv> 32 N

28> A river flowing west to east at speed 3 m/min. A man on the south bank of the river , capable of swimming at 6m/min in still water , wants to swim across the river in shortest time. He should swim in a direction:

i> Due north

ii> 30 degrees west of  north

iii> 30 degrees east of north

iv> 60 degrees east of north

29> In question 28 , If the man wants to swim across the river following the shortest path, then he should swim in a direction:

i> Due north

ii> 30 degrees west of  north

iii> 30 degrees east of north

iv> 60 degrees east of north

30> The resultant of two vectors of unequal magnitudres is equal to the magnitude of the either. The angle between the vector is:

i> 60 degrees

ii> 90 degrees

iii> 120 degrees

iv> 180 degrees

31> In a right handed system:

i> $\hat{j} \times \hat{k} = \hat{i}$

ii> $\hat{i} . \hat{i} = 0$

iii> $\hat{j} \times \hat{j} = 1$

iv> $\hat{k} . \hat{i} = 1$

32> The angle between $\hat{i} + \hat{j}$ and $\hat{i}$ is:

i> $\dfrac{\pi}{6}$

ii> $\dfrac{\pi}{4}$

iii> $\dfrac{\pi}{3}$

iv> $\dfrac{\pi}{2}$

33> The angle between $\hat{i} + \hat{j} + \hat{k}$ and $\hat{i}$ is:

i> $\dfrac{\pi}{6}$

ii> $\dfrac{\pi}{4}$

iii> $\dfrac{\pi}{2}$

iv> $\cos ^{-1} \frac{1}{\sqrt{3}}$

34> If two vectors $\overrightarrow{A} = 2 \hat{i} + 4 \hat{j} - 2 \hat{k}$ and $\overrightarrow{B} = 3 \hat{i} - 2 \hat{j} + n \hat{k}$ are at right angles to each other, then the value of “n” must be:

i> 2

ii> -2

iii> 1

iv> -1

35> Consider a vector $\overrightarrow{F} = 4 \hat{i} - 3 \hat{j}$ , The vector which is perpendicular to $\overrightarrow{F}$ is:

i> $4 \hat{i} + 3 \hat{j}$

ii> $6 \hat{i}$

iii> $7 \hat{k}$

iv> $3 \hat{i} - 4 \hat{j}$

36> The unit vector along $\hat{i} +\hat{j}$ is:

i> $\hat{k}$

ii> $\hat{i} +\hat{j}$

iii>$\dfrac{\hat{i} +\hat{j}}{\sqrt{2}}$

iv> $\dfrac{\hat{i} +\hat{j}}{2}$

37> The unit vector along $\hat{i} +\hat{j} \hat{k}$ is:

i> $\hat{i} +\hat{j} +\hat{k}$

ii> $\dfrac{\hat{i} +\hat{j} +\hat{k}}{3}$

iii> $\dfrac{\hat{i} +\hat{j} +\hat{k}}{\sqrt{2}}$

iv> $\dfrac{\hat{i} +\hat{j} +\hat{k}}{\sqrt{3}}$

38> A vector $\overrightarrow{F_1}$ is along the positive X-axis. If the vector product of it’s with another vector $\overrightarrow{F_2}$ is zero , then $\overrightarrow{F_2}$ could be:

i> $4 \hat{i}$

ii> $( \hat{i} + \hat{j})$

iii> $( \hat{j} + \hat{k})$

iv> $- 4 \hat{i}$

39> Given $\overrightarrow{P} + \overrightarrow{Q} = \overrightarrow{R}$ and “P+Q = R” , then the angle between $\overrightarrow{P}$ and $\overrightarrow{Q}$ is:

i> zero

ii> $\dfrac{\pi}{4}$

iii> $\dfrac{\pi}{2}$

iv> $\pi$

40> Given $\overrightarrow{P} + \overrightarrow{Q} = \overrightarrow{R}$ and $P^2 + Q^2 = R^2$ , then the angle between $\overrightarrow{P}$ and $\overrightarrow{Q}$ is:

i> zero

ii> $\dfrac{\pi}{4}$

iii> $\dfrac{\pi}{2}$

iv> $\pi$

41> Forces $\overrightarrow{F_1}$ and $\overrightarrow{F_2}$ act on a point mass in two mutually perpendicular directions. The magnitude of the resultant force on the point mass will be:

i>  $F_1 + F_2$

ii> $\sqrt{F^2_1 + F^2_2 }$

iii> $F_1 + F_2$

iv> $\sqrt{F^2_1 + F^2_2 - 2.F_1.F_2}$

42> A boat which has a speed of 5 km/hr in still water crosses a river of width 1Km along the shortest possible path on 15 minutes. The velocity of the river in Km/hr is:

i>  1

ii> 3

iii> 4

iv> $\sqrt{41}$

43> A boat is sent across a river with a velocity of 8Km/hr . If the resultant velocity of the boat is 10Km/hr , the velocity of river flow is:

i>  12.8 Km/hr

ii> 6 Km/hr

iii> 8 Km/hr

iv> 10 Km/hr

44> If the position vector of a particle is $\overrightarrow{r} = a \cos \omega t \hat{i} + a\sin \omega t \hat{j}$ then the velocity vector of the particle is:

i> Parallel to position vector

ii> perpendicular to position vector

iii> directed towards the origin

iv> directed away from the origin

45> The angle made by a vector $\overrightarrow{A} = 2 \hat{i} + 3 \hat{j}$ with Y-axis is:

i> $\tan ^{-1} \left(\dfrac{3}{2}\right)$

ii> $\tan ^{-1} \left(\dfrac{2}{3}\right)$

iii> $\sin ^{-1} \left(\dfrac{2}{3}\right)$

iv> $\cos ^{-1} \left(\dfrac{3}{2}\right)$

46> The angle made by the two vectors $\overrightarrow{A} = 3 \hat{i} + 4 \hat{j} + 5 \hat{k}$  and $\overrightarrow{B} = 3 \hat{i} + 4 \hat{j} + 5 \hat{k}$ is:

i> zero

ii> 45 degrees

iii> 90 degrees

iv> 180 degrees

47>  A body considered to move in Y-axis is subjected to a force given by $\overrightarrow{F} = -2 \hat{i} + 15 \hat{j} + 6 \hat{k}$ Newton. What is the work done by the force in moving the body a distance of 10 meters along the Y-axis?

i> 190 J

ii> 160 J

iii> 150 J

iv> 20 J

48> The scalar and vector product of two vectors have magnitude $6\sqrt{3}$ and 6 units respectively. The angle between the two vectors must be:

i> 30 degrees

ii> 45 degrees

iii> 60 degrees

iv> 90 degrees

49> At what angle should the two vectors 2F and $\sqrt{2} F$ act so that the resultant force is $F \sqrt{10}$.

i> 120 degrees

ii> 90 degrees

iii> 60 degrees

iv> 45 degrees

50> A vector $\overrightarrow{A}$ of magnitude $5\sqrt{3}$ units and another vector $\overrightarrow{B}$ of magnitude $10$ units are inclined to each other at an angle of 30 degrees. The magnitude of the vector product of these two vectors is:

i> 10 units

ii> $5\sqrt{3}$ units

iii> $25\sqrt{3}$ units

iv> 75 units

1>iii     2>iv     3>ii     4>iv     5>iii

6>iii     7>i     8>ii     9>iii     10>i

11>i     12>iii     13>iv     14>iv     15>ii

16>iii     17>ii     18>iii     19>ii     20>i

21>iv     22>iii     23>i     24>iii     25>ii

26>iii     27>iii     28>i     29>ii     30>iii

31>i     32> ii     33>iv     34>iv     35>iii

36>iii     37>iv     38>iv     39>i     40>iii

41>ii     42>ii     43>ii     44>ii     45>ii

46>i     47>iii     48>iii     49>iv     50>iii

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